Fracture Propagation Research Articles

Quantification of fracture mechanics with digital image correlation guides the infill design of 3D-printed snack bars with modulated flexural properties

ABSTRACT The ability to design complex infill patterns is unique for 3D food printing to modulate food texture on top of other factors such as processing parameters and structural porosity. This study systematically investigated the impact of infill designs on the flexural properties of 3D-printed snack bars made from pea ingredients. Three-point bending tests revealed that increasing infill angle from 30 to 90 degree resulted in a larger flexural strength but a smaller flexural elongation of the 3D-printed snack bars. However, crossed layer structures did not improve the flexural properties of the samples. Digital image correlation revealed deformation behaviour and fracture propagation of 3D-printed snack bars during mechanical tests. Using the strain maps generated, the designs of the 3D-printed snack bars were modulated to achieve desired flexural properties. Overall, this study shows that it is feasible to customise 3D-printed food texture while maintaining its total calorie, by modifying the infill design.

Study on the Mechanism and Regulation Method of Longitudinal Penetration of Hydraulic Fractures in Multilayered Shale

Summary Shale reservoirs have longitudinally developed multilayered weak surfaces. The strong geological discontinuity and the stress heterogeneity caused by it lead to the complicated morphology of hydraulic fracture propagation, and the longitudinal propagation mechanism of the hydraulic fracture is still unclear. The extended finite element 3D numerical model of the single-cluster fracture and multicluster fracture extension has been established. The effects of vertical stress difference, bonding strength of bedding plane, fracturing fluid displacement, fracturing fluid viscosity, and cluster spacing on fracture propagation morphology are analyzed by numerical examples. The results show that as the vertical stress difference and the bonding strength of the bedding plane increase, the bedding plane becomes more difficult to activate, and the fractures are more likely to realize the longitudinal penetration. As the cluster spacing decreases, the interfracture interference becomes stronger, and the hydraulic fractures are more likely to activate the bedding plane and form the orthogonal network fracture. At a high injection rate, the fracture passes easily through the layer and activates the bedding plane. Low-viscosity fracturing fluid is conducive to the activation of the bedding plane, and high-viscosity fracturing fluid can better achieve fracture penetration. Based on the research results, the fracturing parameters of Well X-1 are optimized, and the fracture monitoring results are in good agreement with the design objectives. This study reveals the longitudinal penetration mechanism of multilayered shale hydraulic fractures and provides a reference for the optimization of hydraulic fracturing parameters of multilayered shale.

Experimental Study of Plugging Agent Particle Size and Concentration on Temporary Plugging Fracturing in Shale Formation

During the temporary plugging fracturing (TPF) process, the pressure response and pumping behavior significantly differ from those observed during conventional fracturing fluid pumping. Once the temporary plugging agent (TPA) forms a plug, subsequent fracture initiation and propagation become more intricate due to the influence of the TPA and early fractures. Factors such as concentration, particle size, and ratio of the TPA notably affect the effectiveness of TPF. This study employs a true triaxial hydraulic fracturing simulation system to conduct TPF experiments with varying particle size combinations and concentrations at both in-fracture and in-stage locations. The impact of different TPA parameters on the plugging effectiveness is assessed by analyzing the morphology of the induced fractures and the characteristics of pressure curves post experiment. Results indicate that combining dfferent particle sizes enhances plugging effectiveness, with a combination of smaller and larger particles exhibiting superior plugging effectiveness, resulting in a pressure increase of over 25.9%. As the concentration of the TPA increases, the plugging fracture pressure rises, accompanied by rapid pressure response and significant plugging effects, leading to more complex fracture morphology. For shale reservoirs, the density of bedding planes (BPs) influences the morphology and width of conventional hydraulic fractures, thereby affecting the effectiveness of subsequent refracturing. Rock samples with a relatively low BP density demonstrate effective plugging initiation both in-fracture and in-stage, facilitating the formation of complex fracture networks. Conversely, specimens with a relatively high BP density exhibit superior plugging effectiveness in-stage compared to in-fracture plugging.

Research on the Interaction Mechanism of Multi-Fracture Propagation in Hydraulic Fracturing

During the hydraulic-fracturing process, stress interference occurs among multiple wells and fractures, potentially affecting the trajectory of hydraulic fracture propagation. Previous studies have largely overlooked the influence of proppant support stresses on the trajectories of fracture propagation. This paper establishes a mathematical model, grounded in the boundary element method, designed to compute the propagation of multiple fractures, considering both proppant support on the fracture surface and dynamic perturbations within the local stress field. The findings of this research reveal that the stress field induced by hydraulic fracturing exhibits dynamic evolution characteristics, necessitating a comprehensive study of the fracture initiation and extension across the entire fracturing time domain. The effect of the residual fracture width under proppant action on the in situ stress field cannot be ignored. During simultaneous fracturing, hydraulic fractures are inclined to propagate in the direction of the maximum horizontal principal stress, particularly as the in situ differential stress escalates. Staggered fracturing between wells has been proven to be more effective than head-to-head fracturing. Simply increasing the well spacing cannot solve the problem of inter-well fracture interference. In zipper fracturing, adjusting the fracturing sequence can inhibit the fracture intersections between wells, thereby controlling the trajectory of fracture propagation. The aforementioned research has considerable significance in guiding the control of fracture morphology during hydraulic-fracturing processes.

Effect of impact-corrosion coupling damage on fatigue properties of 2198-T8 aluminum-lithium alloy

The peeling of aircraft surface paint due to foreign object impact can expose the aluminum–lithium alloy substrate to atmospheric corrosion, resulting in the fatigue performance being affected by the combined effect of impact damage and corrosion damage. In this work, the effects of impact damage and corrosion damage on the fatigue life of 2198-T8 aluminum–lithium alloy sheet were investigated. The strain field distribution of specimens with coupled impact and corrosion damage under cyclic loading was analyzed by Digital Image Correlation (DIC) technique, and the coupling relationship between impact and corrosion damage was analyzed based on the crack propagation path and fracture morphology. The results show that surface corrosion pits depth distribution of impact dents follows the same trend as residual stress distribution. For the coupling damage of the hemispherical punch, the coupled effect between impact damage and corrosion damage is most evident at low impact energy. At higher impact energies, the impact damage dominates the coupling damage. As the salt spray corrosion time increases, the fatigue life decrease rate gradually slows with increasing impact energy, and the impact damage has a greater effect on the fatigue life in the early corrosion stage. Compared to the salt spray corrosion environment at 35 °C, the fatigue life of the specimen at 25 °C increased by a maximum of 50.48 % as the impact energy increased from 10 J to 25 J.

Geomechanical risk assessment of injection test for a carbon storage site appraisal, offshore Northern Territory

A geomechanical study has been conducted to assess the risk of formation fracturing and sanding during a water injection test. Considering the temperature difference between the storage formation and the injection fluid, the cooling effects could lead to a reduction of almost 15% in fracture initiation pressure (FIP). Notably, the FIP for perforations aligned with the maximum horizontal stress direction are lower than the minimum horizontal stress. While injection pressures surpassing FIP might trigger tensile fracturing in specific perforations, fracture propagation from the wellbore remains unlikely if the injection pressure remains below the field’s minimum horizontal stress. The pressure requirements for current envisaged matrix injection rates fall below the estimated FIPs. Consequently, the risk of formation fracturing during the injection test is deemed low. The propensity of sanding during flowback, considering a range of rock weakening and thermal effects of water injection, is also found to be low.

A Study on the Mechanism of Fracture Initiation and Propagation under Multi-Perforation Conditions in Hydraulic Fracturing

To reveal the mechanism of hydraulic fracture initiation and propagation under the conditions of multiple perforations during horizontal well fracturing, we creatively conducted dual-hole fracturing experiments on small rock samples and established a two-dimensional model of a single cluster with multiple perforations in a horizontal well based on the extended finite element method using the fluid–solid coupling equation, which was combined with the basic theory of damage mechanics. The biggest difference from previous research is that this model does not consider the hypothesis of stress shadows and only focuses on studying the initiation and propagation of multiple perforations in one cluster. We studied the effects of perforation parameters, stress state, and injection flow rate on the initiation and propagation of hydraulic fractures using this model. The experimental and simulation results indicate that under multi-perforation conditions, the number of fractures depends on the number of perforations. The simulation results show that when the spacing between perforations increases or the number of perforations reduces, the initiation time of perforation is advanced and the interference between fractures weakens, which is conducive to the initiation and propagation of hydraulic fractures. As the stress difference increases, the initiation time of perforation becomes earlier and the deflection angle of the outermost fractures becomes smaller, which is conducive to the parallel expansion of the fractures. Moreover, although this has little impact on the morphology of fractures with the rise in flow rate in simulation, it is beneficial for improving the initiation and propagation speed of fractures. The length of fractures also increases significantly at the same time point. In addition, both the experiments and simulations revealed that an increase in the flow rate could accelerate the initiation time of fractures. The proposed model can guide fracturing construction to optimize the design of perforation spacing during horizontal well fracturing, which can contribute to reducing development costs and improving the final production.

Simulation of Key Influencing Factors of Hydraulic Fracturing Fracture Propagation in a Shale Reservoir Based on the Displacement Discontinuity Method (DDM)

In the process of the large-scale hydraulic fracturing of a shale gas field in the Weiyuan area of Sichuan province, the quantitative description and evaluation of hydraulic fracture expansion morphology and the three-dimensional distribution law are the key points of evaluation of block fracturing transformation effect. Many scholars have used the finite element method, discrete element method, grid-free method and other numerical simulation methods to quantitatively characterize hydraulic fractures, but there are often the problems that the indoor physical simulation results are much different from the actual results and the accuracy of most quantitative studies is poor. Considering rock mechanics parameters and based on the displacement discontinuity method (DDM), a single-stage multi-cluster fracture propagation model of horizontal well was established. The effects of Young’s modulus, Poisson’s ratio, the in situ stress difference, the approximation angle, the perforation cluster number and the perforation spacing on the formation of complex fracture networks and on the geometrical parameters of hydraulic fractures were simulated. The research results can provide theoretical reference and practical guidance for the optimization of large-scale fracturing parameters and the quantitative post-fracturing evaluation of horizontal wells in unconventional reservoirs such as shale gas reservoirs.

Misorientation Angle Study on Cleavage Fracture Propagation Surfaces of a Grade a Ship Steel, through Charpy and Four-Point Double-Notch Bend Tests

Misorientation Angle Study on Cleavage Fracture Propagation Surfaces of a Grade a Ship Steel, through Charpy and Four-Point Double-Notch Bend Tests

A comparative analysis of 3D woven honeycomb-based aircrew helmet liners against Nomex and Aluminum alternatives

This study investigates the energy dissipation efficiency of an aircrew helmet liner developed using 3D woven honeycomb structural composites compared to different commercially available honeycomb liner materials such as Nomex, and Aluminium. In contrast to liners with discrete density differences, the use of a honeycomb-based liner reduces the concern about delamination, back face deformation and fracture propagation. The research involves comparing several parameters related to crashworthiness, such as specific energy absorption (SEA), crush force efficiency (CFE), and margin of safety, which are crucial for head protection and ensuring helmet injury tolerance. These parameters play a vital role in assessing the ability of different configurations of the honeycomb liner during impacts. Flatwise compression and dynamic impact tests were conducted to evaluate the helmet liner’s performance while maintaining consistency in the helmet shell component. Finite element analysis (FEA) and 3D x-ray Tomography techniques were utilized to analyse the back face deformation (BFD) at high-velocity impact and the internal damage resulting from impacts on the helmet liners, respectively. The results revealed that the 3D woven honeycomb liner configuration performs optimally in terms of energy absorption by demonstrating sufficient and balanced competency across these three critical factors. Additionally, the simulation result revealed that the 3D woven honeycomb liner exhibits wave propagation. This phenomenon enhances its energy absorption capacity and reduces back-face deformation attributed to its crushing behaviour. This research offers valuable insights for improving the performance of aircrew helmet liners, with a particular focus on utilizing 3D woven honeycomb liners featuring 3D woven solid structure to maintain exceptional structural integrity.

Pore structure response at different scales in coal to cyclical liquid nitrogen treatment and its impact on permeability and micromechanical properties

The methane in the coal seams of abandoned mines is a valuable natural gas resource. However, the ultra-low permeability of coal seams restricts the extraction of coalbed methane. The liquid nitrogen fracturing technology is a novel approach suitable for enhancing the permeability of coal seams in abandoned mines. The ultra-low temperature could potentially facilitate the growth and propagation of pores and fractures in coal seams. In this study, we observed inconsistent alterations in coal properties measured by multiple instruments at different scales, whether in dry or wet coal specimens. This suggests that the mechanisms influencing the pore structure due to LN2 treatment differ across various scales in dry and wet coal specimens. For dry specimens, heterogeneous thermal deformation and freezing shrinkage exhibited opposing effects during LN2 treatment. Thermal stress-induced micro-fractures might counteract the freezing contraction of micropores in coal matrices, preventing a significant decrease in coal macropores and fractures. In wet specimens, the effects of LN2 treatment on wet coal specimens were predominantly controlled by frost heaving. However, due to low water saturation, LN2 treatment had negligible effects on coal micropores, even in the presence of local frost heaving. In field applications, water migration from smaller to larger pores could further diminish the impact of LN2 treatment on micropores.

Study on the fracture propagation of ground fissures with syn-depositional structure in Fenwei Basin, China

In Fenwei Basin, most of the tectonic ground fissures show characteristics of growth faults on the section. They continue to destroy the engineering properties of soil at different depths. This has introduced significant security risks to the construction processes of deep underground spaces. However, there are few studies have been conducted on syn-depositional ground fissures. Therefore, in this study, a physical simulation test was used to study the fracture propagation of syn-depositional ground fissures. The characteristics of sections and surface fractures were analyzed. The engineering properties of model soil were divided into bad and poor areas. The syn-depositional ground fissure fracture propagation process was divided into five phases. The results show that soil profile exhibited a composite Y-shaped fracture morphology. Syn-deposition affects the fracture angle and healing state of fractures. The soil strain and surface displacement were positively correlated with the number of deposition layers. The conclusions of this study provide a theoretical geological basis and practical engineering significance for design of deep underground space structures.

Analytical modeling and simulations of dynamic mode-III fracture in pre-stressed dry sandy elastic continuum

A mathematical model has been developed to investigate the SIF (stress intensity factor) and COD (crack opening displacement) for the propagation of mode-III fracture influenced by propagating SH-wave in a pre-stressed dry sandy elastic continuum. The Wiener-Hopf mathematical method along with the Fourier integral transform (FIT) technique have been successively implemented to obtain the solution of the boundary value problem associated with the mathematical model. Furthermore, the closed form solutions of SIF and COD for non-static and static conditions of mode-III fracture have been obtained, and are found to be in well agreement with the existing results present in the literature. The sound effects of various affecting parameters viz. horizontal and vertical (compressive/tensile) pre-stresses, crack depth, and crack velocity on SIF and COD have been explored. In order to delineate the influences of these aforementioned parameters on SIF and COD graphically, numerical simulation has been accomplished.

Multiple hydraulic fracture propagation simulation in deep shale gas reservoir considering thermal effects

Deep and ultra-deep shale gas will gradually become the focus of unconventional oil and gas resources in the petroleum industry. In the development of shallow shale reservoirs, the multi-cluster hydraulic fracturing of horizontal wells is the commonly applied technique to create a network of fractures and achieve reservoir stimulation. However, for deep shale reservoirs, the behavior of multiple hydraulic fracture propagation is affected by stress interference between fractures. On the other hand, it is also influenced by the temperature disturbances caused by the injection of low-temperature fracturing fluids into high-temperature formations and the resulting thermal effects. Currently, most research on multiple hydraulic fracture propagation in shale only considers the interaction between fluids and solids while neglecting thermal effects. Therefore, based on the displacement discontinuity method, finite volume method, and finite difference method, this study established a numerical model for the non-planar propagation of multi-cluster hydraulic fractures in deep shale, considering the thermal effects. And the model was validated through numerical solutions of the temperature field and double-fracture propagation. Moreover, the number of fracture clusters, pumping rate, and formation temperature were selected as influencing factors, and the differences in multiple hydraulic fracture propagation with and without considering thermal effects were analyzed. The results show that as the formation temperature increases, the thermal effects become more significant, leading to greater differences in the morphology of multi-cluster fractures. Moreover, the thermal effects are more significant when the formation temperature exceeds 90 °C. Additionally, appropriately reducing the number of fracture clusters or increasing the pumping rate can to some extent mitigate stress interference between fractures and promote uniform fracture propagation. The findings of this study contribute to understanding the influence of thermal effects on multiple hydraulic fracture propagation and provide theoretical basis for the efficient development of deep shale gas.

Research on active load reducing optimization strategy for 6061Al low cycle fatigue cropping process based on crack propagation mode transformation

Low cycle fatigue cropping technology is a new type of cropping technology with advantages such as no chip waste and low load need. Numerous studies have shown that increasing the fatigue frequency or increasing the displacement load can improve the cropping efficiency, but at the same time, it will reduce the quality of the cross-section and cannot achieve a balance between high efficiency and high quality of cross-section. In response to this issue, this paper found the phenomenon of transition of fracture modes (from fatigue mode to tensile fracture mode) of 6061Al material in LCFC process, and proposed the Active Load Reducing Optimization Strategy for 6061Al in LCFC, which achieves a significant improvement in quality of cross-section with a slight loss of cropping efficiency. Firstly, this paper studied the crack fracture mechanism of 6061Al bar under different displacement loads in the LCFC process. It was found that the transition of crack propagation mode in 6061Al- LCFC process was the main reason for the increase in cross-section roughness. The crack propagation mode changed from fatigue propagation to tensile fracture propagation during the LCFC process, and the roughness of the area significantly increased under the tensile fracture propagation mode. Further research has found that the fundamental reason for the contradiction between the cropping efficiency and section quality of 6061Al is the change in time of crack propagation mode transition and tensile fracture zone area under different displacement loads. Finally, the LCFC process was modeled in a time dimension using acoustic emission(AE) technology, and it was divided into three stages according to the AE signals and the fracture mechanism. As a result, an active load reducing optimization strategy for LCFC process was developed to delay the occurrence of tensile fracture propagation modes. Experiments have shown that compared to the traditional LCFC cropping strategy using constant displacement loads, the active load reducing strategy proposed in this paper can reduce the proportion of tensile fracture area, achieve a significant improvement in quality of cross-section with a slight loss of cropping efficiency, thus achieving a balance between efficiency and section quality to some extent. At the same time, an LCFC process section quality efficiency evaluation index with dual weights of efficiency and section quality has been proposed, which can assist in selecting LCFC active load reducing strategy parameters with consideration of efficiency and section quality weights.

Study on the Interaction Propagation Mechanism of Inter-Cluster Fractures under Different Fracturing Sequences

Horizontal-well multi-cluster fracturing is one of the most important techniques for increasing the recovery rate in unconventional oil and gas reservoir development. However, under the influence of complex induced stress fields, the mechanism of interaction and propagation of fractures within each segment remains unclear. In this study, based on rock fracture criteria, combined with the boundary element displacement discontinuity method, a two-dimensional numerical simulation model of hydraulic fracturing crack propagation in a planar plane was established. Using this model, the interaction and propagation process of inter-cluster fractures under different fracturing sequences within horizontal well segments and the mechanism of induced stress field effects were analyzed. The influence mechanism of cluster spacing, fracture design length, and fracture internal pressure on the propagation morphology of inter-cluster fractures was also investigated. The research results indicate that, when using the alternating fracturing method, it is advisable to appropriately increase the cluster spacing to weaken the inhibitory effect of induced stress around the fractures created by prior fracturing on subsequent fracturing. Compared to the alternating fracturing method, the propagation morphology of fractures under the symmetrical fracturing method is more complex. At smaller cluster spacing, fractures created by prior fracturing are more susceptible to being captured by fractures from subsequent fracturing. The findings of this study provide reliable theoretical support for the optimization design of fracturing sequences and fracturing processes in horizontal well segments.

How are microstructural defect interactions linked to simultaneous intergranular and transgranular fracture modes in polycrystalline systems?

The major objective of this investigation is to fundamentally understand and predict how intergranular (IG) and transgranular (TG) fracture modes nucleate and propagate in f.c.c. polycrystalline systems due to defects, such as total and partial dislocation densities and grain boundary (GB) structures and misorientations. A dislocation density crystalline plasticity (DCP) formulation based on the evolution and interaction of total and partial dislocation densities was integrated with a recently developed fracture approach to investigate the fracture nucleation and propagation of simultaneous multiple fracture events, including both IG and TG fracture events. The aggregate grains and GB orientations and morphologies are based on EBSD measurements that are representative of polycrystalline copper aggregates with a broad range of random high angle and low angle GBs. The predictions indicate that dislocation density pileups induce IG fracture due to interrelated stress, slip, and total and partial dislocation density accumulations and interactions for both high angle GBs (HAGBs) and low angle GBs (LAGBs). TG fracture nucleation and propagation occurred due to normal stress accumulations, which exceeds the fracture stress, along cleavage planes. Furthermore, it is shown how IG cracks transition from the GB plane to the cleavage planes as cracks nucleate and propagate. Accumulated plastic zones due to different slip system activities can impede and blunt crack propagation and fronts. These plastic zones form due to high Lomer and Shockley partial dislocation densities. These predictions, which are consistent with experimental observations, provide a fundamental understanding of how simultaneous failure modes initiate and propagate for physically representative microstructures.

Influences of clean fracturing fluid viscosity and horizontal in-situ stress difference on hydraulic fracture propagation and morphology in coal seam

The viscosity of fracturing fluid and in-situ stress difference are the two important factors that affect the hydraulic fracturing pressure and propagation morphology. In this study, raw coal was used to prepare coal samples for experiments, and clean fracturing fluid samples were prepared using CTAB surfactant. A series of hydraulic fracturing tests were conducted with an in-house developed triaxial hydraulic fracturing simulator and the fracturing process was monitored with an acoustic emission instrument to analyze the influences of fracturing fluid viscosity and horizontal in-situ stress difference on coal fracture propagation. The results show that the number of branched fractures decreased, the fracture pattern became simpler, the fractures width increased obviously, and the distribution of AE event points was concentrated with the increase of the fracturing fluid viscosity or the horizontal in-situ stress difference. The acoustic emission energy decreases with the increase of fracturing fluid viscosity and increases with the increase of horizontal in situ stress difference. The low viscosity clean fracturing fluid has strong elasticity and is easy to be compressed into the tip of fractures, resulting in complex fractures. The high viscosity clean fracturing fluids are the opposite. Our experimental results provide a reference and scientific basis for the design and optimization of field hydraulic fracturing parameters.

Crack propagation mechanism of smooth blasting holes for tunnel excavation under high in-situ stress

Smooth blasting is an important excavation method in tunnel construction, creating a smooth and even excavation profile during the excavation process. In this study, the influence of in-situ stress, hole spacing, and radial decoupling coefficient on the superposition of blasting stress and the cracking characteristic between holes were investigated by using integrated analytical and numerical analyses (FDEM). Based on those results, the design of smooth blasting parameters considering the influence of in-situ stress were suggested, and verified against the data collected during the blasting excavation of diversion tunnel at Jinping II hydropower station. The results indicated that the propagation of blast-induced fractures are significantly influenced by the insitu stress conditions, tending to extend towards the direction of the maximum principal stress thus the holes should be arranged along the direction of the maximum principal stress to ensure the formation of cracks between holes and smooth excavation of the wall.

Optimization design of plugging agent dosage and application of deep shale gas inner-diversion fracturing

China boasts abundant deep shale gas resources with considerable development potential. However, the weak brittleness and large horizontal stress contrast of deep shale rock may restrain the complex fractures network extension during hydraulic fracturing. To address this challenge, the inner-diversion fracturing technique is widely employed, facilitating the formation of a complex fractures network. Numerous theoretical studies emphasize the pivotal role of plugging pressure exerted by temporary plugging agents within fractures in enhancing deep shale stimulation performance. However, various types of temporary plugging agents with different plugging performances make it difficult to determine the optimal dosage of temporary plugging agents before fracturing operation. This study considered the dynamic propagation of fractures affected by the coupling of the induced stress from clustered fractures and the fluid pressure within the fractures into the mathematical model, based on rock mechanics theory. Subsequently, the inner-diversion capability testing instrument was utilized to evaluate the critical plugging pressure of several common temporary plugging materials. By integrating on-site data from temporary plugging and inner-diversion fracturing operations in the Southern Sichuan deep shale gas reservoir with this approach, the optimal dosage of temporary plugging agents in the operational scheme was refined. The fracturing operation curves demonstrate that the temporary plugging and inner-diversion pressure significantly increased after pumping the temporary plugging agent, indicating the hydraulic fractures successful plugging and a large-scale complex fractures network extension. This underscores the potential effectiveness of the temporary plugging dosage optimization method for inner-diversion fracturing. Furthermore, this study not only provides important guidance for optimal design but also mitigates the operational risks of inner-diversion fracturing in deep shale gas horizontal wells.